Relatively to point i), common GGA or hybrid functionals fail in capturing vdW interactions, but several correction schemes are available at very little additional computational cost. Some of the most widely employed methods include a parametrization of dispersion interactions by adding a potential term \(V(\mathbf {r}_{ij})=-C_{6}/r^{6}_{ij}\)  among atoms. The parametrization of the coefficients \(C_{6}\)  is then carried out according to different schemes, such as the Tkatchenko's or Grimme's methods[1]}, [2]}. These methods account for the screening effect of covalent bonds on local atomic polarizability, which reflects on a reduction of the coefficients \(C_{6}\)  with respect to the reference gas-phase atomic values. Concerning point ii) of correctly describing the strongly correlated states of \(d\) - or \(f\) -elements, DFT is known to perform poorly, and methods such as CASSCF[3]} or DMRG[4]} are often used to fix the problem. These methods are however not suitable for large periodic systems and the use of GGA DFT is once again a forced choice for current algorithms and computational power. Fortunately, however, the shortcoming of GGA DFT in representing the correct magnetic states of open shell metal compounds does not seem to dramatically spread to the prediction of forces, and phonons calculations of magnetic molecules' crystals based on DFT are routinely carried out with good success. Finally, in relation to point iii), it should be noted that a structural optimization leads to a zero-temperature geometry. The latter does not correctly describe the compound structure in the same thermodynamics condition of the experiments. The inclusion of finite-temperature effects can be accomplished by accounting for anharmonic contributions to the crystal potential energy surface. Anharmonic effects in crystals can be modelled in different ways, including quasi-harmonic approaches, perturbative treatments, or by running molecular dynamics simulation in the presence of a thermostat[5]}. The importance of including anharmonic effects into the description of phonons for spin-phonon coupling calculations has only recently be pointed out[6]}, [7]}, [8]} and a systematic investigation is yet to be presented, but it represents an important area of investigation.
